24 citations · 75 across the 6 of their papers we have counts for
6 papers
Para-Bannai-Ito Polynomials
Jonathan Pelletier, Luc Vinet, Alexei Zhedanov
New bispectral polynomials orthogonal on a Bannai-Ito bi-lattice (uniform quadri-lattice) are obtained from an unconventional truncation of the untruncated Bannai-Ito and complemen…
Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
Éric-Olivier Bossé, Luc Vinet
The analytic specifications of photonic lattices with fractional revival (FR) and perfect state transfer (PST) are reviewed. The approach to their design which is based on orthogon…
Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard r…
A Bochner Theorem for Dunkl Polynomials
Luc Vinet, Alexei Zhedanov
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural condition…
Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
Luc Vinet, Alexei Zhedanov
We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yiel…
Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
Luc Vinet, Alexei Zhedanov
We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, expli…